I think you need to do a little thinking on what kind of character you really want to have.
Psychopathy and persons with an Antisocial Personality Disorder exist in real life and you can go to real life psychiatry forums or clinics or anywhere they'd allow you to get some real life research done for more information if you are concerned about authenticity.
Research into treatment in these cases are still ongoing, there's not a lot, and it's more accurate to say that it's not treated than it's not treatable in an offhand way.
Case studies are also a good way to go. It's not hard. You can familiarize yourself with the information within some months just by some YouTube psychology videos, cracking open a textbook or two, (not really the DSM - this is mostly just diagnostic criteria, which won't really help you understand it) and accessing some journal articles. Or you can find someone qualified to consult with if you have any psych major friends perhaps. Or you may be able to audit some lectures... The information is out there, you just have to find/gather it and read up.
When you understand psychopathy/ASPD, the next step should be to blend it into a fictional character. Decorate, exaggerate, embellish as it suits your needs while keeping it organic and real. Some information on archetype, maybe. Character motivations/needs.
With enough of a foundation, it will become very easy to sink into your character and understand how his gears work and what makes him tick. You can go through worksheets and really stretch him out and make him "live-in" so that it doesn't look like you are writing with a checklist of symptoms in mind.
Your story has to guide your character and vice versa, otherwise, you won't have an organic character, just an assimilation of loose ideas which I doubt you want.
In a more commercial work, there's often the "popular" psychopath/sociopath who isn't really clinically, "in real life" either a psychopath or a sociopath.
They self-declare themselves as sociopaths in order to be edgy or cool, when clinically, they'd be more likely to be someone on the autistic spectrum, or someone with another personality disorder (narcissist/borderline) gone homicidal and psychotic.
Fantasy (especially grimdark fantasy) and murder mysteries are full of these types. The grimdark ones burn villages and only pull their mask out on special occasions while the murder mystery ones have a high IQ and plan things out with clever twists whose masks slip maybe once or twice total.
If this is the case of what you're getting at with "untreatable", masked, uber-logical, frequently agitated psychopaths, you should consult TVtropes.com.
Audiences now have expectations as to what they're supposed to get when they see a synopsis that reads "there's a psychopath" in this." Is your story a slow police drama like Shield or will there be chainsaws falling from stairs in an overblown meta-satire like American Psycho?
I'd advise you to take a couple of steps back, gather information and let the whole process resolve itself into something natural.
It's really a peeve of mine when characters come out like "Hey, I'm the psychopath in the story. See my evil works. I revel in your awe."
There are lots of conditions out there that result in apathy, people lacking empathy or being overly logical or pathologically detached from reality. If you're going for authenticity, the only solution is research. If you can't put yourself in his mind frame now, you just have to rub the lotion in until you feel comfortable enough with it.